Abstract: Literature suggests that steady chemical patterns could serve as an explanation for pattern formation in biology. One way to generate these spatial patterns is by the Turing instability in reaction-diffusion equations. In this report we explain some of the theory of the Turing instability with a focus on a prototype model by Schnakenberg. The parameter values that allow for pattern formation are investigated in more detail. Numerical explorations using an IMEX-pseudospectral method are made to test predictions for the one-dimensional Schnakenberg model.